Optical control of Faraday rotation in hot Rb vapor

We demonstrate controlled polarization rotation of an optical field conditional on the presence of a second field. Induced rotations of greater than $\pi /2$ rad are seen with a transmission of $95\%$, corresponding to a ratio of phase shift to absorption of $40\pi$. This combination of large, controlled rotation and low loss is well suited for the manipulation of light pulses.

Figure 1

An illustration of energy-level configurations leading to circular birefringence. (i) The energies of the $\sigma$ transitions are degenerate, and the states are equally populated: no asymmetry is seen for circularly polarized light. (ii) An applied magnetic field lifts the degeneracy to such an extent that, while the ${\sigma }^{+}$ transition is resonant, the ${\sigma }^{-}$ is detuned further from resonance. (iii) While both transitions are resonant, a population difference is present, leading to birefringence.

Figure 2

(i) Probe signal produced by scanning the probe versus red detuning ${\Delta }_P$, from the $D_1$ ${}^{87}\mathrm{Rb}$ $F=2\to F^{\prime }=1$ transition in units of Doppler width $\Delta {\omega }_D=2\pi \times 571\hspace{0.5em}\mathrm{MHz}$. The red and dashed black curves show, respectively, the measured and theoretical differencing signal (left axis). The dot-dashed blue curve shows the total transmission through the cell (right axis). (ii) The measured rotation angle (data points) and theoretical rotation (curve). The temperature of the cell is ${115}^{°}$C and the applied magnetic field is 204 G.

Figure 3

Schematic of the experimental apparatus. A probe beam passes through a polarization beam splitter (PBS), providing linearly polarized light. The beam is attenuated with a neutral-density filter (ND) before passing through a heated vapor cell. A half-wave plate ($\lambda /2$) is used to control the polarization angle of the light before it is analyzed with a PBS and collected on a differencing photodiode (PD). A control beam is linearly polarized and counterpropagated at a small crossing angle. A small fraction of the beam is used to perform sub-Doppler spectroscopy in a reference cell.

Figure 4

(i) Differencing signal of the $D_1$ probe versus $D_2$ control field blue detuning ${\Delta }_C$. The power of the control field is 9 (solid red) and 30 mW (dashed blue). The experiment cell is at a temperature of $~$115 ${}^{°}$C, with a 204 G applied magnetic field. The probe is at a red detuning of $~$2.9 Doppler widths (1.7 GHz), marked in Fig. 2. In the absence of the control field, the differencing signal is given by the horizontal dashed black line. (ii) Transmission of the control-laser light through the room-temperature natural-abundance reference cell (dashed black) and the ${}^{87}\mathrm{Rb}$ experiment cell (blue). Control detuning is with respect to the weighted $D_2$ line center.

Figure 5

Differencing signal of the $D_1$ probe versus red detuning ${\Delta }_P$. The dashed black curve shows the experimentally measured signal in the absence of the $D_2$ control field (from Fig. 2). Plots (i) and (ii) illustrate the effect of optical pumping on the probe signal when the 38-mW control field is fixed at detunings $A$ and $B$ given in Fig. 4. The temperature and applied magnetic field are the same as in Fig. 2.

Figure 6

Measured rotation angles $\theta$ versus red detuning ${\Delta }_P$ of the $D_1$ probe. The angles are calculated from the zero crossings and extrema of Fig. 5 for no optical control (squares) and red-detuned (circles) and blue-detuned (triangles) control fields. The curves are from theory. Vertical bars show the detunings at which $\pi /2$ rotations can be obtained by switching among the three curves.

Figure 7

(i) Rotation difference between the cases with and without the optical control field, obtained from the experimental data shown in Fig. 6. Curves $A$ (blue) and $B$(red) are, respectively, for blue and red detunings. Curve $C$ (black) shows the rotation difference between blue and red detunings. (ii) Measured transmission of the linear probe in zero magnetic field. (iii) Figure of merit of the switching scheme: The curve was obtained from theory; the points show measured data. The dashed vertical line marks the limit close to resonance where the probe polarization becomes elliptical owing to circular dichroism (differential absorption of the left- and right-circularly polarized field components).